For the function f:[1,∞)→[1,∞) defined by f(x)=(x-1)⁴+1, among the two statements: (I) The set S= [1,∞): f(x)=f⁻¹(x) contains exactly two elements, and (II) The set S= [1,∞): f(x)=f⁻¹(x+1) is an empty set,

(D) neither (I) nor (II) is TRUE

Sets, Relations and Functions: JEE Main 2026 Mathematics question

JEE Main 2026 · 4 Apr, Evening shift · Q1

JEE Main 20264 Apr, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002

For the function

f:[1,\infty)\to[1,\infty)

defined by

f(x)=(x-1)^4+1

, among the two statements: (I) The set

S=\{x\in[1,\infty): f(x)=f^{-1}(x)\}

contains exactly two elements, and (II) The set

S=\{x\in[1,\infty): f(x)=f^{-1}(x+1)\}

is an empty set,